Solving an exponential equation - Check my method

Hi,

I'm new to the forum, but decided to give it a try now, because I can't seem to get around what I'm doing wrong. I'm revising for my IB finals and can't seem to get this one question down, which is from a past final exam:

But this doesn't check out with the original equation, because it comes to 256 = 40
It's been a while since we did logarithms and exponents, so I might be doing something incorrect. So please correct me where I'm wrong.

I'm new to the forum, but decided to give it a try now, because I can't seem to get around what I'm doing wrong. I'm revising for my IB finals and can't seem to get this one question down, which is from a past final exam:

So the question is: Solve the equation

My method:
4^(x-1) = 2^x+8
4^(x-1) = 2^x+2^3
2^(2(x-1)) = 2^x+2^3
2^(2x-2) = 2^x+2^3
log 2 (2^(2x-2)) = log 2 (2^x) + log 2 (8) Unfortunately, no. This is the mistake.Taking logs of both sides will lead you to a dead end here. Review this stage carefully, you've not taken logs of the right hand side correctly.